Crate tensor4all_tensorci 

Tensor Cross Interpolation (TCI) library

This crate provides tensor cross interpolation algorithms for efficiently approximating high-dimensional tensors as tensor trains. Given a function f(i_1, ..., i_N) defined on a discrete multi-index grid, TCI finds a low-rank TensorTrain approximation by evaluating only a small subset of the total entries.

Algorithms

Entry point	Algorithm	State type	Notes
crossinterpolate2	TCI2 (two-site)	TensorCI2	Primary, actively maintained
crossinterpolate1	TCI1 (one-site)	TensorCI1	Legacy, kept for compatibility

TCI2 uses MatrixLUCI for pivot updates and supports batch evaluation, global pivot search, and two pivot search strategies (PivotSearchStrategy::Full and PivotSearchStrategy::Rook).

Quick start

use tensor4all_tensorci::{crossinterpolate2, TCI2Options};
use tensor4all_simplett::AbstractTensorTrain;

// Function to interpolate: f(i, j) = i + j + 1
let f = |idx: &Vec<usize>| (idx[0] + idx[1] + 1) as f64;
let local_dims = vec![4, 4];
let first_pivot = vec![vec![1, 1]];

let (tci, _ranks, errors) =
    crossinterpolate2::<f64, _, fn(&[Vec<usize>]) -> Vec<f64>>(
        f,
        None,
        local_dims,
        first_pivot,
        TCI2Options::default(),
    )
    .unwrap();

// Check convergence
assert!(*errors.last().unwrap() < 1e-6);

// Evaluate through the tensor train
let tt = tci.to_tensor_train().unwrap();
let val = tt.evaluate(&[2, 3]).unwrap();
assert!((val - 6.0).abs() < 1e-10); // f(2,3) = 2+3+1 = 6

Related crates

• tensor4all_tcicore – low-level matrix CI primitives and CachedFunction
• tensor4all_simplett – the TensorTrain data structure produced by TCI
• tensor4all-quanticstci – higher-level quantics TCI on discrete or continuous grids (wraps this crate)

Re-exports

pub use error::Result;

pub use error::TCIError;

pub use globalpivot::DefaultGlobalPivotFinder;

pub use globalpivot::GlobalPivotFinder;

pub use globalpivot::GlobalPivotSearchInput;

pub use globalsearch::estimate_true_error;

pub use globalsearch::floating_zone;

pub use optfirstpivot::opt_first_pivot;

pub use tensorci1::crossinterpolate1;

pub use tensorci1::SweepStrategy;

pub use tensorci1::TCI1Options;

pub use tensorci1::TensorCI1;

pub use tensorci2::crossinterpolate2;

pub use tensorci2::PivotSearchStrategy;

pub use tensorci2::Sweep2Strategy;

pub use tensorci2::TCI2Options;

pub use tensorci2::TensorCI2;

Modules

error

Error types for tensor cross interpolation operations

globalpivot

Global pivot finder for the TCI2 algorithm.

globalsearch

Post-hoc error estimation for tensor train approximations.

integration

Numerical integration using TCI and Gauss-Kronrod quadrature.

optfirstpivot

Utility for optimizing the first pivot for tensor cross interpolation.

tensorci1

TensorCI1 – One-site Tensor Cross Interpolation algorithm (legacy).

tensorci2

TensorCI2 - Two-site Tensor Cross Interpolation algorithm

Structs

CachedFunction

A wrapper that caches function evaluations for multi-index inputs.

IndexSet

A bidirectional index set for efficient lookup

Enums

CacheKeyError

Errors that can occur during cache key computation.

Traits

CacheKey

Trait for cache key types used in flat-index computation.

IndexInt

Trait for index element types.

Scalar

Common scalar trait for matrix and tensor operations.

Type Aliases

LocalIndex

A single site-local index.

MultiIndex

A multi-index: a vector of site-local indices.